We collected species occurrence information (species presence data with geographical coordinates) from the Global Biodiversity Information Facility (GBIF, http://www.gbif.org/; data accessed in 2021) database, using family names in The Plant List (TPL, http://www.theplantlist.org/). ¹ Then we used the “CoordinateCleaner” R package to clean the original occurrence data, discarding coordinates that matched the centroids of countries, capitals, known botanical institutions, and GBIF headquarters, zero coordinates and equal latitude and longitude, as well as those falling in the sea (Zizka et al., 2019). We also excluded occurrences where geographical information was missing or duplicated. We then selected widely distributed families, which were distributed in at least the main continents (excluding Antarctica) and across a wide range of latitudes (spanning more than ninety degrees). We focused on wide-ranging families because narrow-ranging plant groups were likely to have restricted ranges, and so their responses to the environment might be simplified across scales or may not be detected at varying spatial scales. We ultimately obtained 205 families, 688 genera, and 1610 species for the subsequent analyses ( Supplementary Information Appendix S2 ).

We obtained information on climatic, topographic, and soil variables, which are crucial in determining plant distributions at multiple scales. Temperature and precipitation variables were derived from WorldClim (http://www.worldclim.org/). Solar radiation was obtained from Global Solar Alta 2.0 (https://globalsolaratlas.info/). ² We collected the properties of topsoil (e.g., total nitrogen, pH) from two databases, the Harmonized World Soil Database (HWSD; https://www.fao.org/soils-portal/data-hub/soil-maps-and-databases/harmonized-world-soil-database-v12/en/; Fischer et al., 2008) and the Global Soil Database (http://globalchange.bnu.edu.cn/research/soilw; Shangguan et al., 2014). We derived topographic variables (i.e., elevation, aspect, and slope) from the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM). All the environmental variables ( Supplementary Information Appendix S1: Table S1.1 ) were processed into 30 arc-second rasters, and the values were extracted according to the geographical locations of the corresponding plant taxa. We conducted principal component analysis (PCA) for variables from the same resource (e.g., temperature and precipitation from WorldClim) or of similar type (e.g., soil properties from two databases) to avoid spurious collinearity among original variables and to reduce environmental dimensions for subsequent analyses. For 19 climate variables (indexes about temperature and precipitation) in worldClim, we used the first three principal components (PCs)that accounted for > 80% of the variance. For 15 soil variables, we used the first five soil PCs. which accounted for > 70% in soil variables ( Supplementary Information Appendix S1: Tables S1.3 , S1.4 ). We ultimately obtained 12 environmental variables (including eight PC axes) for subsequent analysis ( Supplementary Information Appendix S1: Table S1.2 ).

We assessed the effects of spatial scales based on different spatial extents at the regional scale. We first randomly sampled 500 locations across the globe ( Figure 1 ). These locations distribute across all the main continents and cover most ecological biomes (both Whittaker biomes, Whittaker, 1975, and WWF biomes, Olson et al., 2001; Supplementary Information Appendix S1: Figure S1.1 ). Frequents of different biomes were not same due to varying areas of these biomes across the globe and different data density in GBIF database (even when we have conducted data manipulation to reduce sample bias). Then, we created “plots” around the center of each location, spanning 1° × 1°, 2° × 2°, 3° × 3°, 4° × 4°, 5° × 5°, 6° × 6°, 7° × 7°, 8° × 8°, 9° × 9°, or 10° × 10° (i.e., 10 levels of spatial extents at the regional scale). We considered all occurrences of a plant taxon (only at the family, genus, or species level) in each plot with a specific spatial extent as an individual dataset. In this case we can analyze scales effect by controlling the locations (as random effects in the mixed effect model below). Plant taxa with less than three occurrences within a sampled plot were removed from the datasets. We further selected the plots with at least three taxonomic groups at the corresponding taxonomic scale to satisfy the random forest analysis. We focused on the extent instead of the grain because plant occurrence was obtained as scattered data (with geographical coordinates) and was processed to the same resolution as environmental variables. For a comparison at a specific location, we assessed the difference in relative environmental effects across 10 levels of spatial extents and 3 levels of taxonomic ranks.

We used random forest to assess the relative importance of the environmental factors affecting plant distribution at multiple scales. The random forest algorithm is a combination of tree predictors, where each tree relies on the values of a random vector that are sampled independently and with the same distribution for all trees in the forest (Breiman, 2001). It is more precise and applicable when dealing with large multivariate data (nonlinear, correlated, or biased) than classical statistical methods, and hence it is widely used in classification and regression, especially the selection of variables in ecology (Cutler et al., 2007; Genuer et al., 2010). We conducted random forest for every dataset (species data at one particular spatial and taxonomic scale in a location) separately. In each random forest model, we used presence–absence of 0.5° × 0.5° grid cells as dependent variables, and associated environmental variables (12 variables in every grid corresponding to occurrence) as explanatory variables. Presence points were defined as occurrence records of a plant taxon (at family, genus, or species levels), while absence points were represented by the same number of presence points (pseudo-absences) that were randomly selected from background grid cells for every focal taxon (Barbet-Massin et al., 2012). Datasets with less than three occurrences were excluded due to the requirements of random forest.

We performed random forest algorithms using the “randomForest” package in R 3.6.1 (Liaw & Wiener, 2002). The random forest takes bootstrapped samples from the original dataset to build a decision tree, and then average the predictions of each tree for a final model. The number of sampled trees in our study was set to 500 for every test. We used the mean decrease Gini (MDG) to assess the relative contribution of every environmental factor. It measures the total decrease in node impurities (averaged over all trees) from splitting on the variable, so it reflects the overall importance of every variable from the model. Larger MDG values indicate greater importance (Hong et al., 2016). We calculated the MDG value for every environmental factor at every spatial and taxonomic scales. To facilitate comparison among datasets of different scales, we standardized the MDG values to the range of 0 to 1 in every dataset using the equation MDG_{Standardized,i} = MDG_i/( ∑ i 15 M D G i ). For species occurring in the same location at the same spatial and taxonomic scale, we conducted the random forest algorithm separately for every species (or genus or family) taxon respectively. Thus, we obtained over 15000 datasets at different spatial and taxonomic scales to run random forest in total.

To evaluate the model performance, we used the out of bag (OOB) error rates from random forest model. It is an estimate of error rate, calculated as (1 – accuracy), which means that lower OOB indicated higher accuracy. We also calculated the cross-validation out of bag (CV OOB) error rates as supplementary, using “rf.crossValidation” functions in “rfUtilities” R package (Evans & Cushman, 2009).

We used mixed effect models to test the effects of spatial and taxonomic scales on the relative importance of environmental factors (represented as MDG values of every variable at specific scales from the random forest). We performed different models for three types of variables (climate, soil, and topography) and for every single factor (12 variables, including PCs). First, we classified the environmental variables into three groups (i.e., climate, soil, and topography) and conducted the analysis separately for each group. For each group, we added all variables’ relative importance (e.g., the sum of relative importance of all three climate PCs and solar radiation) at one location at one specific spatial and taxonomic scale to represent the relative effect of this group, viewed as independent variables in our mixed effect models. We calculated the average MDG values of all species in the same dataset (i.e., one plot with the one specific spatial and taxonomic scales) and variable group before modeling. The fixed effects included the spatial and taxonomic scales, and the interaction between spatial and taxonomic scales. The random effects included sampled locations and their two- interactions with spatial and taxonomic scales. We then also repeated these analyses separately for each environmental variable, in which we set spatial and taxonomic scales and their interaction as fixed effects, and sampled locations and their two-way interactions with spatial and taxonomic scales as random effects.

We conducted the mixed-effect model with the “lmer” R package (Pinheiro et al., 2021). All the mixed effect models meet the assumption of linear mixed effect models by checking distributions of residuals-fitted values. The R square of every mixed effect model was calculated using the ‘r.squaredGLMM’ function in the ‘MuMIn’ package (Bartoń, 2013) in R (R Core Team, 2023), based on a conditional R square concerned with variance explained by both fixed and random factors (Nakagawa & Schielzeth, 2013).

Climatic variables had a larger impact on plant distributions when the spatial and taxonomic scales increased at spatial extents larger than 4° × 4°. The results overall support our hypotheses (H1) relating to the spatial and taxonomic scale-dependence patterns of climate effects on plant distributions within limited scales. These results are congruent with past descriptions and analyses of the vegetation of the world (as far back as Von Humboldt, 1805). High spatial variation in climate conditions at large spatial scales may possibly explain the spatial scale-dependence of climatic effects on plant distributions. However, stochasticity appeared at fine scales (<4° × 4°), where the trends in climate effect with spatial scale varied significantly among different taxonomic levels. These may due to the variety of local processes (e.g., stochastic processes) at finer spatial scales. Thus, it is more reliable to use climate variables for predicting plant distribution patterns at a relatively broad spatial scale, where climatic constraints such as temperature extremes and light intensity restrict plant radiation across the globe.

Plants have evolved traits to adapt to climate change and extreme climate (e.g., episodic freezing) or have dispersed to more suitable areas (Zanne et al., 2014). The relative importance of climatic effects among different taxonomic levels shows that the response of plants to climate may be more distinct between families than within families (e.g., among species), indicating that the climate-related traits of plants are the consequence of long-term adaptive evolution (Zanne et al., 2014).

Soil was more important at finer spatial scales and at lower taxonomic levels (i.e., species>genus>family), which aligns well with our hypothesis (H2). The effects of soil on plant distributions diminished at large spatial extents with greater soil heterogeneity ( Figure 2B ). Soil heterogeneity at fine spatial scale may cause variation in the strength of ecological processes that shape local plant distributions and coexistence, such as the root absorption of nutrients, microbe shifts, and mycorrhizal symbiosis (Smith & Read, 1997; Callaway, 2007; Wang et al., 2019).

Soil effects were stronger at relatively lower taxonomic scales ( Figure 2B ), suggesting that fine-scale processes related to soil (e.g., plant–soil feedback) are more likely to vary among species than families. This indicated that these processes may be driven by recent events and thus may be more dynamic. Despite the general decreasing trends in soil effects with spatial and taxonomic scales, specific factors within the category showed different patterns ( Figures 2B , 3 ). For example, the relative importance of PC4 and PC8 (mainly representing soil texture and gravel, respectively) increased with spatial extents. This implies that internal processes related to soil niche are complex and varied.

The topographical effects on plant distribution were relatively intricate and unpredictable across spatial scales ( Figures 2C , 3 ). Topographical factors affect plant distributions by causing changes in other ecological conditions (Irl et al., 2015; Slaton, 2015; Muscarella et al., 2020), such as the microclimate and edatope of plant habitats along an elevational gradient, which is nonlinear and difficult to predict. Nevertheless, their influences are perhaps strongly related to the presence of montane species with a limited range in mountainous areas. Thus, topographical effects should not be continually increased at large scales beyond the geographical range of mountains. This was confirmed in our analysis whereby the trends in topographical effects that increased with spatial scale flattened at spatial extents larger than 4° × 4° (with the exception of 6° × 6° for species; Figure 2C ).

The influence of topography on plant distributions also emanates from the unique evolutionary histories of montane ecosystems (Muellner-Riehl et al., 2019). Topographical factors showed more influence at the species level than at the genus and family levels ( Figure 2C ). This result supports our hypothesis of the taxonomic scale-dependence of topographical effects (H3), revealing the impact of evolutionary history on montane floras. Topography probably had a stronger effect on species than on families because montane floras tend to be related to nearby lowland floras. On the contrary, most of the variation in plant distributions caused by topographical changes has occurred recently in evolutionary history (Kelly & Goulden, 2008).

Generally, climate variables’ relative importance is larger than topography and soil ( Figure 2 ), which is similar to results of our former study on environmental effects on global plant distributions (Huang et al., 2021). However, the detection of environmental effects depends on the methods we use. Additional analyses of other measurements (e.g., MaxEnt model) also show similar trends in relative environmental effects changing with spatial and taxonomic scales, though different in importance value to some degrees ( Supplementary Information Appendix S3 ).

Nevertheless, it is still difficult to know how multi-scale processes interact with each other that shape the scale-dependence patterns in our study using large-scale occurrence data. For example, global and regional changes in biological diversity are the origins and consequences of fine-scale phenomena (Levin, 1992) or assemblage-level processes (e.g., biotic interaction and dispersal). The interplay of multi-scale and cross-scale processes is actually comprehensive and poorly understood, and further studies integrating community ecology, macroecology, and macroevolution are needed.